Three resistors (10, 15, and 20 ohms) are connected in parallel to a 24 V source.

Question

Three resistors (10, 15, and 20 ohms) are connected in parallel to a 24 V source. Show all work for credit.

What is the voltage drop across each resistor?

What is the current through each resistor?

What is the current through the battery?

What is the equivalent resistance of the circuit?

How much energy is consumed by each resistor during a 10 minute time period?

Answer 1

Voltage drop for each is 24 V because of parallel connection

i₁ = v/R₁ = 24V/10 ohms = 2.4 A, i₂ = v/R₂ = 24V/15 0hms = 1.6 A; i₃ = v/R₃ = 24V/20 ohms = 1.2 A

Current through battery i = 2.4A + 1.6A+ 1.2A = 5.2 A

R = v/i = 24V/5.2A = 4.615 Ohms

E₁ = v²/R₁·t = 24²/10·600 = 34560 J

E₂ = v²/R₂·t = 24²/15·600 = 23040 J

E₃ = v²/R₃·t = 24²/20·600 = 17280 J ·